Implementing the Science of Math in a Culturally Sustainable Framework for Students With and at Risk for Math Learning Disabilities

Abstract

This article focuses on implementing the Science of Math through a culturally responsive framework designed to support culturally and linguistically diverse students in math classrooms. We consider the influence of (second) language acquisition and instructional environments for students in addition to specific ways to increase instructional engagement with considerations of students’ cultural identity, prior experiences, and dual language development. Key features of the culturally responsive math instruction framework for dual language learning students with and at risk for math disabilities include utilizing culturally and linguistically appropriate assessment, anti-biased contextual supports, linguistics supports within math curriculum, and sustaining home-school collaborations. Implications for applying the framework for math instruction are discussed.

Mr. Cruz is a first-year special education teacher at Sagebrush Independent School District, an urban district located in the southwestern region of the United States. His elementary school serves a high population of diverse Spanish-English dual-language learners, many of whom are from marginalized and underserved communities. Although Mr. Cruz heard the common misconception that “math is a universal language,” he knows many students from culturally and linguistically diverse backgrounds have a history of difficulty with learning mathematics. Mr. Cruz is familiar with current effective mathematical instructional practices but is wondering how he can embrace a culturally responsive framework to equitably serve his students.

Students identified as culturally and linguistically diverse continue to increase across the nation (U.S. Department of Education, National Center for Education Statistics [NCES], 2021). Children considered to be culturally and linguistically diverse (CLD) are those who are from racial/ethnic minority background and/or those students who speak, read, write, or understand a language other than English in their homes (NCES, 2020; Sullivan, 2011). As such, children who have not yet achieved proficiency in English (i.e., English learners [ELs], emergent bilinguals [EBs], dual-language learners, multilinguals) would also be considered as CLD students.

Historically, CLD students have encountered disparate educational opportunities and resources (Klingner et al., 2006). These educational experiences often result in lower outcomes, placing many CLD students at risk for learning disabilities, specifically in math. These academic outcomes have led to the paradoxical overrepresentation and underrepresentation of CLD students in special education identification (Sullivan, 2011). For example, research has found that Black, Hispanic, and Native American students were overidentified for special education programs under the high-incidence categories (e.g., specific learning disabilities, emotional disabilities; Sullivan, 2011). Students acquiring English, however, were underrepresented in special education programs in primary grades but overrepresented after third grade (Samson & Lesaux, 2009).

Clearly, CLD students are a heterogeneous group, and not all students (multilingual students included) experience mathematic difficulties and/or specific learning disability in math. Math disability (MD) refers to students diagnosed as having a specific learning disability (Individuals with Disabilites Education Act, 2004, Sec. 300.8[c][10]), a disorder in one or more of the basic psychological processes with significant difficulties in math calculations. Overall, variability has existed in how students have been identified with a learning disability in math, which has added to the challenge in effective identification and intervention for students with MD (Mazzocco & Myers, 2003).

Historically, children have been identified as having a learning disability in math given a significant discrepancy between IQ and achievement (discrepancy model; Hallahan et al., 2013). However, many students may demonstrate low performance in math without a diagnosis of a MD. The term “at risk for MD” refers to students who struggle with math and are at risk for identification of a specific learning disability in math (Nelson & Powell, 2018). The 25th percentile cutoff score on standardized measures has been commonly used to identify children at risk (e.g., Fletcher et al., 1989; Swanson et al., 2013). Considering the challenges many CLD students can face with mathematics, it is important to highlight some of the unique instructional considerations for CLD students with and at risk for MD and identify factors of effective math instruction.

The Influence of Language

Upon entering school, children with a native language other than English in the home are often identified as “English learners.” However, the usage of this term has begun to shift to “emergent bilinguals” to highlight the unique linguistic strengths these children bring with them (see García et al., 2008). As mentioned earlier, children who have not yet achieved proficiency in English (i.e., ELs, EBs, dual-language learners, multilinguals) would fall under the umbrella of CLD. Emergent bilingual students specifically, though, are a heterogeneous group with varied language proficiency levels and differing levels of language exposure to English. When we think about language, there are two key areas to consider: receptive language and expressive language. Receptive language refers to what a child can understand what is being communicated to them, or their comprehension of language. This is often captured by a child’s ability to follow directions and their responses to questions. Expressive language refers to a child’s ability to speak, or use, language. Expressive language is often examined through activities ranging from naming objects, sentence generation tasks, or story retells. These two areas of language differ in development, with individuals initially demonstrating stronger receptive language than expressive language in the earlier stages of language development (e.g., Fenson et al., 1994). However, EB children will have different levels of ability with their expressive and receptive language development in each of their languages due to the distribution of their learning in each language (e.g., Oller & Pearson, 2002). This is key for educators to consider because mathematical learning and the new vocabulary terms that are associated with that learning take only a small fraction of the school day.

Instructional Environments

There are a range of instructional environments in which an EB student might be placed upon entering the school system. It is important to provide context for the different academic programs for students who enter the U.S. educational system with minimal development of the English language. Depending on the students’ language skills, parent enrollment information, school and district policies, children with similar skills may be placed into different educational classroom environments. There are a variety of instructional delivery models a school, district, or state may choose to implement for their EB students, varying from English as a second language pull-out to structured immersion programs. Each educational model comes with its own set of theoretical views on how a child may expect to learn and develop the academic content. Not only are there a range of instructional delivery models, but within each, there are a variety of ways in which a school may decide to deliver content in one language compared to another. What further complicates these models is some may provide a 90–10 or 50–50 model of language input through the elementary years. In other words, classroom instruction is weighted toward one language in the 90–10 model, with 90% of instruction in one language and 10% in the other, or it might be evenly split in input between the two languages for a 50–50 model (Boyle et al., 2015). As an EB student progresses through the elementary years, they may encounter changes in the amount of input they hear in each language (i.e., 90–10 in first grade, 80–20 in second grade, 70–30 in third grade, etc.). Therefore, it is imperative educators are aware of their EB students’ prior educational experiences, including language of instructional content in math, to have a more comprehensive understanding of what may be impacting their learning.

Culturally Responsive Instruction

A culturally responsive framework for math instruction fosters equitable environments for learning by taking into consideration the unique assets, experiences, and needs of culturally and linguistically diverse students with and at risk for specific learning disabilities in math (Abdulrahim & Orosco, 2020; Gay, 2002; Utley et al., 2011). Culturally responsive instruction as it pertains to math specifically does not replace the current knowledge base for effective instruction for students with or at risk for MD, such as explicit instruction, attention to conceptual understanding, schema instruction, the use of visual representations and supports, helping students to articulate math concepts, and progress monitoring (Fuchs et al, 2008; Kong et al., 2021; Woodward et al., 2012). Rather, culturally responsive math instruction is a framework for delivering and sustaining equitable and effective instruction for all students by integrating what we already know about effective math instruction for students with MD with culturally responsive instruction (see Figure 1; Utley et al., 2011). This framework is comprised of four key features (See Table 1): (a) using culturally and linguistically appropriate mathematic assessment tools and approaches (Arizmendi et al., 2021), (b) including antibiased contextual supports within math curriculum (Abdulrahim & Orosco, 2020; Driver & Powell, 2017), (c) providing linguistic supports (Driver & Powell, 2017), and (d) sustaining home-school collaborations (Abdulrahim & Orosco, 2020; Utley et al., 2011).

Figure 1

Examples of instructional emphases in culturally responsive math teaching compared to typical math teaching practices

Table 1

Examples of Culturally and Linguistically Responsive Activities

Area	Specific skill	Sample activity
Culturally and linguistically appropriate assessment	Providing assessments that consider the child’s language ability and cultural experiences	• Teacher provides directions and explanation of task in comprehensible language or with native language support. • Assessments are controlled for vocabulary and language ability if appropriate. • Each assessment targets one skill to identify areas of need.
Antibiased contextual supports	Integrating students’ experiences and cultural background into math instruction	• Teacher introduces the concept of part and whole by displaying pictures of food that can be cut into equal parts (e.g., apples, oranges). • Students provide examples and draw pictures of food that may be shared from their respective cultures. • Utilize student examples to cut foods into equal parts.
Linguistic supports	Providing language support in math instruction	• Teacher explicitly preteaches academic and mathematic specific vocabulary by: ° modeling pronunciation ° providing a student-friendly definition ° providing examples of appropriate usage ° providing native language translation if appropriate. • Teacher models strategy usage in comprehensible language.
Home-school collaborations	Sustaining positive relationships between school and home	• Send home positive notes of successes (translated if necessary). • Provide visual representations of progress in math (e.g., progress monitoring graphs). • Ask caregivers and students to identify ways math is used in the community. • Value home input on expectations and responsibilities.

Culturally and Linguistically Appropriate Assessment

The first key feature of culturally responsive math instruction is culturally and linguistically appropriate assessment. Because many CLD students have not yet acquired the linguistic ability level to perform in the classroom as their monolingual English-speaking peers, CLD students often struggle when they enter an English-based classroom (August & Shanahan, 2008). When CLD students begin to fall behind academically, they may sometimes be referred for special education services and are inaccurately diagnosed as needing these services based on performance on English-only measures. This is problematic because it leads to a confound with language ability and discounts the distribution of skills across two or more languages. As stated in Table 1, culturally and linguistically appropriate assessments provide assessment that considers the students’ native languages and cultural experiences. Testing in English only to determine eligibility for special education services often leads to the reported overrepresentation of CLD children in special education (e.g., Artiles et al., 2005; Sullivan, 2011), most commonly being identified with a learning disability.

Although the process for eligibility determination may vary, standardized assessments are typically administered by multilingual school psychologists or special education teachers to determine achievement in specific areas. By acting as an advocate for the child, a special education teacher can verify that assessments are conducted in both English and the students’ native language. For example, several math calculation and word problem standardized assessments are available in both English and Spanish translations, such as the English Calculation and Applied Problems subtests from the Woodcock-Johnson IV (Schrank & Wendling, 2018) and the parallel Spanish Calculos and Problemas Aplicados subtest from the Batería III Woodcock-Muñoz (Woodcock et al., 2005). While bilingual assessment performed by a professional who is fluent in the student’s native language is considered best practice, it is certainly possible that standardized assessments may not be available in the child’s native language or a professional who is fluent in the child’s language is not available. In these instances, the teacher is encouraged to use a trained interpreter or utilize alternative procedures for assessment (Ortiz, 2004). Alternative and informal assessments may include the use of curriculum-based measures to determine the skills the child can do. For example, a teacher can collect work samples in specific math areas (determining 1–1 correspondence by matching objects, calculation problems increasing in complexity, measurement using various tools, nonverbal reasoning activities) that act as informal assessments.

In addition to appropriate initial assessments to identify students who are culturally and linguistically diverse with MD, ongoing progress monitoring to make data-based instructional decisions has been shown to be a vital component of interventions for students with and at risk for MDs (Fuchs et al., 2008; Powell et al., 2021). Curriculum-based measures are typically utilized to measure progress in a variety of math skills, including early numeracy skills (e.g., magnitude judgment), calculation, and concepts and applications. Unfortunately, typical assessment tools may not fully capture the skills of students with culturally and linguistically diverse backgrounds (Alt et al., 2013). Culturally and linguistically appropriate assessment tools and approaches are critical in obtaining accurate and valid data. Consider curriculum-based measures that offer ongoing progress monitoring in both English and a student’s native language (e.g., i-Ready Math) when available. If the curriculum-based measures in the student’s native language are not available, consider utilizing informal assessments that assess the same skill each time.

In order for Mr. Cruz to accurately assess his students to determine eligibility for services, he will utilize assessments that are culturally and linguistically appropriate. Because Spanish is the first and primary language spoken in his student’s home, Mr. Cruz decides to assess the same skill in the student’s native language in addition to English. For example, Mr. Cruz used the Spanish standardized assessments (e.g., Batería Woodcock-Muñoz) and curriculum-based measures (e.g., i-Ready Math) in conjunction with the English counterparts. In addition to providing valuable information for the individualized education program team, Mr. Cruz found difficulties persisted in both languages, which signaled to him that rather than an issue with language acquisition, this student was experiencing mathematical difficulties. If this student who performed poorly on English measures but not on Spanish measures, Mr. Cruz would know that this student’s difficulty in math may be attributed to language needs. In this case, Mr. Cruz would continue to assess the student’s math skills in Spanish to accurately measure their actual math ability.

In addition to linguistically appropriate assessments, Mr. Cruz decided to utilize informal assessments of word problems in the classroom in the students’ native language because he can adapt to control for general academic vocabulary, reading level, or references to cultural experiences or biases. For example, a question on a unit test read “On Sunday, Ted went parasailing at a lake. In 4 minutes, he passed by 4 buoys and 3 docks. How many buoys would he pass in 16 minutes?” Because this problem assumes relevant background knowledge to effectively understand the nature of the item, Mr. Cruz decided to change the references in the word problem to one that is more familiar to his students who reside in an urban environment. “On Monday, Ted walked to school. In 4 minutes, he passed by 4 stop signs and 3 traffic signal lights. How many stop signs would he pass in 16 minutes?” Mr. Cruz noticed when he replaced references in the problem with ones his students were more familiar, his students did not have to stop to ask what “buoy” or “parasailing” meant and could get straight to the task he intended to assess.

Antibiased Contextual Supports

Another key feature of culturally responsive math instructional practices includes antibiased contextual supports in math curriculum and interventions. As stated in Table 1, contextual supports in math instruction provide supports that integrate the cultural background and experiences of the students. Reflect on one’s own external and internal cultural identity, including language, values, expectations, gender roles, and patterns of communication (Utley et al., 2011). Recognizing one’s own cultural experiences and backgrounds, teachers can identify and appreciate how their students’ experiences and backgrounds affect behaviors and performance in the classroom while maintaining high expectations for all students. For example, some students from CLD backgrounds may feel uncomfortable with direct forms of communication or questioning teachers in the classroom. This can be a result of cross-cultural communication differences or sociolinguistic differences, such as a reluctance to participate in front of others due to their own challenges with communicating in English. Communication challenges can be remediated by letting students know ahead of time when they will be called to participate. Recognizing one’s own cultural background, approaching students’ culture with curiosity, and asking students to share about themselves allows the teacher to learn about the child’s experiences while also collecting information to utilize as potential examples or illustrations in classroom activities.

Next, when developing contextual supports in math curriculum, attend to students’ funds of knowledge while avoiding racial stereotypical depictions (Esteban-Guitart & Moll, 2014). An examination of research conducted on culturally responsive math teaching revealed that incorporating students’ experiences and cultural background into math instruction facilitated positive self-perceptions and engagement (Abdulrahim & Orosco, 2020). Provide positive multicultural examples from the students’ lived experiences. This highlights students and families’ math skills and resources embedded in everyday activities that may have gone unacknowledged, helping to build on students’ existing knowledge. Stereotypical depictions can occur in illustrations if it is assumed that all students with a certain cultural background have the same characteristic. Stereotypes can be avoided by utilizing illustrations from students’ specific experiences that have been shared with the class.

Planning for his upcoming math lesson, Mr. Cruz previews the questions for the next lesson. Mr. Cruz wants to teach how to solve multistep word problems while integrating students’ background knowledge and experiences. He comes across this question. “Three art students are touring Paris for the summer. They each paid $22 to visit the Eiffel Tower, $11 for the art museum, and $6 a scenic boat ride. How much do the students spend altogether? Explain.”

Thinking about his students, he knows that three students from his class attend an afterschool science camp, so the first thing he does to address this is to adjust the context of the problem to connect to students and facilitate engagement and positive multicultural examples. “Mateo, Jasmine, and Gabby [names from class] are attending afterschool science camp. During camp, they each had to collect 22 leaves, 11 rock specimens, and 6 insects to investigate. How many items do the students need to collect altogether? Explain.”

Mr. Cruz decides to embed culturally appropriate visual representations to provide a conceptual foundation utilizing the concrete-representational-abstract framework, which he knows has been shown to be effective for students at risk for MD (Bouck et al., 2018; Flores, 2010; see Table 1). He has prepared these items for each table group to demonstrate the multiple steps of the problem utilizing concrete representations.

Mr. Cruz primes the students by saying, “Remember we are working on word problems that require multiple steps in order to solve. I’ll explain and demonstrate an example for how to solve this problem. You will work in your table groups to show what the problem looks like using the items in front of you. Next, Andrea will show us how to solve the first step of the problem, and Alfonso will help us with the second step of the problem. I’ll give you a few minutes to look at the question and talk it over with your table in case you have any questions that I can answer before we walk through the problem with the class.”

By preparing the students and setting clear expectations, Mr. Cruz eliminates some of the anxiety that may come along with mathematical problem solving and the part of the problem that asks students to “explain” their thinking. Working in smaller groups prior to sharing their thoughts in the larger setting provides students more time to process and generate verbal responses. He is also allowing for a variety of ways for students to participate in the math activity, recognizing the diverse cultural background of his students while maintaining high expectations for all.

Linguistic Supports

Math is often thought of as being a universal language, meaning that it can be understood regardless of the language one speaks based on its symbolic and numerical visual nature (e.g., Cavanagh, 2005; Lee & Lee, 2017; Morita-Mullaney et al., 2021; Waller & Flood, 2016). However, math requires additional language-specific vocabulary learning. For example, for a foundational math symbol like “+,” the terms “add,” “plus,” “sum,” “in all,” “more than,” and “altogether” (among others) can be used to represent just one individual mathematical process. For a child learning math in their nonnative language, this means that there are at least six new words being learned to refer to one single concept. Furthermore, when complex sentence processing is introduced in the mid-elementary years via word problems, there is an additional cognitive load of sorting through multiple, complex sentence structures on top of understanding and applying the correct meaning to the individual words in each sentence. Thus, similar to cultural contextual support, teachers can provide linguistic supports in math interventions for students from CLD backgrounds (Hughes et al., 2016; Powell et al., 2019).

As shown in Table 1, linguistic supports provide language-specific supports in math instruction. Examples of linguistic supports include preteaching vocabulary, labeling items in English and students’ native languages, providing visual supports, and providing student-friendly definitions. Providing these supports before, during, and after instruction reduces the need for students to simultaneously learn academic vocabulary and math content.

To reduce language-processing load (Alt et al., 2014; Arizmendi et al., 2021), Mr. Cruz begins the lesson by reading the word problem aloud for the whole class while projecting the problem and pointing to each individual word while reading to assist with decoding, identifying, and defining words and assisting with the comprehension of the item (e.g., Hall et al., 2019). After reading the problem, he reminds the students once again. “Remember, we are working on word problems that require more than one step to solve correctly. In this problem, we have a number of items and three students. What is the question asking? The question is asking us if each of the students have this many items, how many items do we have altogether? Can you work in your groups to show me the two steps that you would need to take to solve this problem?”

Progressing in the lesson, Mr. Cruz knows that bridging the content and language to be understood is important. He integrates native-language supports during math instruction by encouraging students to engage in high-level mathematical discussions with their peers in small groups in their native language as he circles the table groups. Mr. Cruz notices that his students use a variety of strategies, including verbal strategies, visual items (drawing pictorial representations of the items in the word problems), and gestures. During this time, he checks in with the two students he called on earlier (Andrea and Alfonso) to ensure that they are ready to discuss their thoughts with the whole class.

When the class regroups, Mr. Cruz cues Andrea and Alfonso to share their thinking by providing the following sentence stems, “The first/next step of the word problem is ____. I know this because ____.” Mr. Cruz allows opportunities for comprehensive language building and acquisition while providing structure for rich mathematical conversations, which may have been supported by native-language supports in initial discussions with peers.

Home-School Collaborations

Finally, culturally responsive instruction is highly collaborative in nature, sustaining positive relationships between the school and home (Table 1). First, engage in early and frequent positive communication with families. Certainly, language may be a barrier in communication in some instances. Teachers may need to have written communication translated and rely on intercultural communication (Díaz-Rico, 2014). At the beginning of the semester, learn about preferred methods of communication through direct contact with families or by sending a brief questionnaire to families regarding preferred language of communication, with both languages represented in the questionnaire (e.g., “I prefer communication in English” followed by “Yo prefiero comunicación en Inglés” or “I prefer communication in Spanish” followed by “Yo prefiero comunicación en Español”). If there are a variety of first languages represented in the classroom, questionnaires or materials should accommodate for all parents to be able to access the materials.

Additionally, curriculum could incorporate expertise from the community into math lessons. Reciprocally, teachers could create opportunities for authentic practice of math outside of “math class” alone. Just as a child’s sharing of experiences and cultural knowledge is valuable, a family may be able to impart knowledge about math experiences in the home and cultural background. For example, consider assigning a family project in which the family investigates together how math is used in their home in various ways. A sample question assignment such as “Show 3 ways in which you use measurement in your home or community. You may take a picture, write what you did, or draw a picture.” allows a variety of response formats and creativity. Nurturing family engagement and stressing the importance of the family’s native language could also encourage continued multiliteracy.

Mr. Cruz may send weekly, biweekly, or monthly updates regarding the content being taught in the classroom and share insights related to their child’s progress. The development of free online translation services, such as the TalkingPoints app or Google Translate, has allowed frequent communication with families possible even if a teacher is not multilingual. This collaboration can help engage parents in the content and can reinforce learning in the home. For example, the content of the current week’s lesson is multistep word problems. Mr. Cruz might suggest that a parent engage with their child as part of a homework assignment by providing structured activities that ask their child to add how many items of choice they could find in their room. After finding items in the home, sentence stems for writing multistep word problems can be provided. “In one room, I have (number) shirts, (number) toys, and (number) pillows. In another room, I have (number) shirts, (number) toys, and (number) pillows. Write the question that asks how many items altogether. Then solve the problem together.” This can bring math outside of the classroom and into the home in day-to-day activities to continue building the mathematical language.

Conclusion

Overall, providing evidence-based math instructional practices in a culturally responsive framework offers an approach that could benefit students with and at risk for MDs from many diverse backgrounds. Culturally responsive math instruction provides equitable opportunities for students who are culturally and linguistically diverse by accurately identifying skills and difficulties using appropriate assessment practices, utilizing contextual and linguistic supports, and promoting home-school collaboration.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Jennifer E. Kong

Jennifer E. Kong, Chapman University, Orange; and Genesis D. Arizmendi and Christian T. Doabler, The University of Texas at Austin.

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